WASHINGTON — President Trump’s longtime lawyer, Michael Cohen, secretly recorded a conversation with Trump two months before the presidential election in which they discussed payments to a former Playboy model who said she had an affair with Trump, according to lawyers and others familiar with the recording.

The FBI seized the recording this year during a raid on Cohen’s office. The Justice Department is investigating Cohen’s involvement in paying women to tamp down embarrassing news stories about Trump before the 2016 election. Prosecutors want to know whether that violated federal campaign finance laws, and any conversation with Trump about those payments would be of keen interest to them.

The recording’s existence appears to undercut the Trump campaign’s denial of any knowledge of payments to the model. And it further draws Trump into questions about tactics he and his associates used to keep aspects of his personal and business life a secret. And it highlights the potential legal and political danger that Cohen represents to Trump. Once the keeper of many of Trump’s secrets, Cohen is now seen as increasingly willing to consider cooperating with prosecutors.

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The former model, Karen McDougal, says she began a nearly yearlong affair with Trump in 2006, shortly after Trump’s wife, Melania, gave birth to their son Barron. McDougal sold her story for $150,000 to The National Enquirer, which was supportive of Trump, during the final months of the presidential campaign, but the tabloid sat on the story, which kept it from becoming public. The practice, known as “catch and kill,” effectively silenced McDougal for the remainder of the campaign.

Rudy Giuliani, Trump’s personal lawyer, confirmed in a telephone conversation Friday that Trump had discussed payments to McDougal with Cohen in person on the recording. He said it was less than two minutes long, said Trump did not know he was being recorded, and claimed that the president had done nothing wrong.

Giuliani said there was no indication on the tape that Trump knew before the conversation about the payment from the Enquirer’s parent company, American Media Inc., to McDougal.

“Nothing in that conversation suggests that he had any knowledge of it in advance,” Giuliani said.

Giuliani initially indicated the men discussed a payment from Trump to McDougal — separate from the Enquirer’s payment — to buy her story. Later, he said that Trump and Cohen had actually discussed buying the rights to McDougal’s story from the Enquirer, a move that would have effectively reimbursed the newspaper for its payments to her.

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That payment was never made, Giuliani said, adding that Trump had told Cohen that if he were to make a payment related to McDougal, to write a check rather than send cash, so it could be properly documented.

Neither of Giuliani’s descriptions of the conversations explains why, when The Wall Street Journal revealed the existence of the AMI payment days before the election, Trump’s campaign spokeswoman, Hope Hicks, said, “We have no knowledge of any of this.” She said McDougal’s claim of an affair was “totally untrue.”

Cohen’s lawyers discovered the recording as part of their review of the seized materials and shared it with Trump’s lawyers, according to three people briefed on the matter.

“Obviously, there is an ongoing investigation, and we are sensitive to that,” Cohen’s lawyer, Lanny J. Davis, said in a statement. “But suffice it to say that when the recording is heard, it will not hurt Mr. Cohen. Any attempt at spin cannot change what is on the tape.”

Cohen rejected repeated requests for comment. Trump ignored shouted questions about it from reporters as he left the White House on Friday afternoon and departed for a weekend at his golf club in Bedminster, N.J.

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David J. Pecker, the chairman of AMI, is a friend of Trump’s, and McDougal has accused Cohen of secretly taking part in the deal — an allegation that is now part of the FBI investigation.

Karen McDougal sold her story to The National Enquirer, which kept it from becoming public.

“It can’t be more than a minute and a half,” Giuliani said, referring to the length of the conversation. “Twice someone walks in — someone brings soda in for them. It’s not some secret conversation.”

He added: “Neither one seems to be concerned anyone would hear it. It went off on irrelevant subjects that have nothing to do with this. It’s a very professional conversation between a client and a lawyer and the client saying, ‘Do it right.' ”

Because the tape showed Trump learning about the AMI payment, it actually helps Trump, Giuliani argued. “In the big scheme of things, it’s powerful exculpatory evidence,” he said. A person close to Cohen disputed that claim but would not elaborate.

The recording is potential evidence in the campaign finance investigation, but became tied up in a legal fight over what materials are protected by attorney-client privilege and thus off limits to prosecutors. It is not clear whether a federal judge has ruled on whether prosecutors can listen to the recording.

For a decade, Cohen served as one of Trump’s most trusted fixers, aggressively taking on journalists, opposing lawyers and business adversaries. He frequently taped his conversations, unbeknown to the people with whom he was speaking. New York law allows one party to a conversation to tape conversations without the other knowing.

Cohen used to say he would take a bullet for Trump, but the relationship soured in the aftermath of the FBI raids in April. In one conversation, Cohen’s lawyers inquired whether Trump planned to pardon him, but Trump’s lawyers gave no indication that the president would do so, according to two people familiar with the discussion.

Cohen has publicly and privately discussed the idea of cooperating with the FBI.

The Cohen investigation began with the special counsel, Robert Mueller, who is investigating the Trump campaign’s links to Russia. But as the Cohen case became increasingly focused on Cohen’s personal business dealings and his campaign activities unrelated to Russia, Mueller referred it to federal prosecutors in Manhattan, who are now leading the investigation.